Question

Question about equation of plane, parametric equations and stuff like that: http://f.imgtmp.com/HIhr6.jpg

Help would be GREATLY appreciated!

Answer 1

personally id create 2 vectors and cross them for the normal vector

Answer 2

can you type up the points for me, its hard to keep track of them

Answer 3

that's to get the first part?

Answer 4

yeah, plane equation

Answer 5

P(-4,-6,2) and Q(-8,-7,0), R(7,3,5)

Answer 6

good, now what im gonna do is define 2 vectors by subtracting one point from the other 2

Answer 7

wait, first let me finish part 1

Answer 8

Q(-8,-7,0) R( 7, 3, 5)
- P(-4,-6,2) - P(-4,-6,2)
-------------------------
-<4, 1, 2> <11,9,3>

these are 2 vectors that reside on your plane between your points

Answer 9

lets cross them for a normal vector

<4, 1, 2>
<11,9,3>
----------
x = (3-18) = -15
y = -(12-22) = 10
z = (36-11) = 25

<-15,10,25> is the normal vector which we can scale down to work with
--------
-5

<3,-2,-5> looks good to me

Answer 10

now, given any point on the plane; they gave you 3 to play with; we can construct the equation as such:

3(x-Px)-2(y-Py)-5(z-Pz)=0

Answer 11

2 secs, i was searching for something. now i can read properly.

Answer 12

id use a simple point like (-8,-7,0)

3(x--8)-2(y--7)-5(z-0)=0

3x+24-2y-14-5z=0

3x-2y-5z+10=0

if i did it right that should be a match to your 3 points

Answer 13

ok so <3,-2,-5> is the normal vector and 3(x-Px)-2(y-Py)-5(z-Pz)=0 is from dot producting it?

Answer 14

in effect yes.

Answer 15

ya i get that part now thank you. :)

Answer 16

what about the line?

Answer 17

gotta dbl chk my plane equation first, im prone to error at my age :)

Answer 18

wolfram likes it :)

Answer 19

so line PQ ... let me see

Answer 20

its a vector addition of P and Q right?

Answer 21

vector subtraction that is and the points themselvs act as defining the vectors

Answer 22

i just pictured like a toddler helping me on the other side :P

Answer 23

and sorry technical issues make it hard to respond fast here

Answer 24

so, P-Q, i did above = <4,1,2> and this needs to be scaled to any length to create the line

t<4,1,2>

now all we have to do is attach it to either P or Q

Answer 25

i'm guessing your older rather than younger

Answer 26

the best thing about today is that im one step closer to death :)

Answer 27

there is a comma between P and Q if that matters.

Answer 28

lol ... well eat healthy, etc

Answer 29

using -8,-7,0 to anchor our line vector to we get:

x = -8 + 4t
y = -7 + 1t
z = 0 + 2t

should be the parametric stuff

Answer 30

if you plug in P for the x y z parts you should come out to t being the same for all parametrics

Answer 31

P=-4,-6,2

-4 = -8 +4t
4 = 4t

t = 1
-7+1 = -6
0+2 = 2... that works for me :)

Answer 32

ok so you used Q to anchor and P works too. just confirmed.

Answer 33

sorry for being delayed.

Answer 34

'sok, this computers getting slow as well

Answer 35

now the next one is perp to L and hits R

Answer 36

wait before that.

Answer 37

i didn't get what you did when you found a value for t and why you did it.

Answer 38

also, i don't recommend you use CRT. rather use LCD screens because they don't harm your eyes or are negligible in comparison. plasmas make radiation that dissipates before harming you so it's acceptable but i'd go with lcd anyways.

Answer 39

just saying.

Answer 40

since im anchored to Q and it has to go thru P then some value of "t" has to remain the same for each parametric in order to come up with the P values. I solved for Px in place of x to see if we can get a t that worked

Answer 41

when t=1 we get Px so i just subbed in t=1 for the others to see if they matched Py and Pz

Answer 42

if we anchored to P, then we would have used Q to test it out with
:)

Answer 43

i see it now :D

Answer 44

so what about the last part?

Answer 45

the last part I believe uses this line vector as a normal vector of this other plane; and this other plane has to hit R so we should just place Rx Ry Rz in the plane equation

Answer 46

passing through means parallel but more precise?

Answer 47

i mean covering it wholly

Answer 48

sooo,

n<4,1,2>, calibrate with R(x,y,z)

4(x-Rx)+1(y-Ry)+2(z-Rz)=0 expanded of course

Answer 49

we want a plane perp to L, not parallel